Cool! It looks like one of those geographical cross-sections I used to see in science class.
Seems a shame to cover it all up. Why not build a ton of rooms and balconies lining the walls, and connect them all with stairs? Then personally I'd just put a big lava lake at the bottom and cover it with glass.
And sounds like you're like me when it comes to tools. Iron and diamond are just too precious to waste on picks, when stone is everywhere and only requires an extra whack or two.